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This paper describes a two-dimensional (plane strain) elastic-plastic finite element model of rolling contact that embodies the elastic-perfectly plastic, cycle and amplitude-independent material of the Merwin and Johnson theory, but is rigorous with respect to equilibrium and continuity requirements. The rolling contact is simulated by translating a semielliptical pressure distribution. Both Hertzian and modified Hertzian pressure distributions are used to estimate the effect of plasticity on contact width and the continuity of the indentor-indentation interface. The model is tested for its ability to reproduce various features of the elastic-plastic indentation problem and the stress and strain states of single rolling contacts. This paper compares the results derived from the finite element analysis of a single, frictionless rolling contact at p0/k = 5 with those obtained from the Merwin and Johnson analysis. The finite element calculations validate basic assumptions made by Merwin and Johnson and are consistent with the development of “forward” flow. However, the comparison also reveals significant differences in the distribution of residual stress and strain components after a single contact cycle.

Measurements of the cyclic stress-strain hysteresis loop shapes of hardened, HRC-62, SAE 52100 bearing steel, derived from torsion tests are presented. These are reduced to 3-parameter, elastic-linear-kinematic hardening-plastic (ELKP) representations. The ELKP behavior and properties of the steel are employed in an elastic-plastic finite element model of two dimensional, rolling contact. The distortion of the rim and the distribution and magnitude of the residual stresses and cyclic plasticity for repeated contacts at a Hertzian pressure of p0 = 3636 MPa (528 ksi), are calculated. The results are compared with the residual stresses and other features observed in the inner raceway of SAE 52100 steel, deep grooved ball bearings. The calculations predict the modest residual stresses observed in the early life: N ≲ 106 contacts. The much higher levels of residual stress that develop in later life: 108 ≲ N ≲ 1010, are shown to be connected with metallurgical changes and an attending volume expansion that are cyclic strain induced. The origins of these stresses and their effect on bearing life are discussed.

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This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.